Soft and hard decision decoding of product codes for communication systems

Zheng Chen, Takaya Yamamoto, Hiraku Okada +2 more

Ferdinand Blomqvist

Abhijeet N. Chavan, Makarand Mohan Jadhav

The most important thing in any communication system is reliable transmission of data. To transmit the data through noisy channel, a redundancy is added before transmission which is known as channel coding. This transmitted data is decoded at the receiver with the help of soft decision decoding or hard decision decoding. Soft decision decoding can be classified as reliability based and code structure based decoding. Reliability in coding theory implies the probability of decoding the bit correctly. Most reliable bits give correct decoding output while less reliable bits are more prone to create errors. Iterative decoder accepts soft inputs-including a priori values-and delivers soft outputs that can he split into: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. The commonly used iterative decoder is sum product belief propagation algorithm. We are extending this analysis to the min-sum algorithm for polar codes. Using polar codes, the sum-product and min-sum algorithms are compared and simulation results are demonstrated.

Hitoshi Tokushige, P C Fossorier Marc, Tadao Kasami

Andrew J. Wong

Very powerful long low-density parity-check (LDPC) codes, such as the ITU G.975.1 Standard (32643, 30592) LDPC Code [1], have been considered for optical communications. Traditional implementations of such long codes result in circuits requiring millions of interconnections, which are not affordable. This thesis investigates the performance of the hard-decision differential decoding with binary message-passing (DD-BMP) algorithm [2], a low-complexity algorithm requiring a minimal number of wires due to its binary messages. Our simulation results for the ITU G.975.1 standard demonstrate that hard-decision DD-BMP algorithm outperforms the results provided in the standard, and that the gap between the decoding performance of hard-decision DD-BMP and hard-decision sum-product is small at high signal-to-noise ratios (SNR). We also present a novel design methodology for implementing a soft-decision decoder by exploiting the code's structure. An implementation-efficient architecture is presented using a partially-parallel adaptation of the min-sum algorithm known as the line-passing algorithm. The line-passing algorithm makes soft-decision decoding available while requiring a minimal number of interconnections, which is attractive for long-haul optical communication systems.

Martin Tomlinson, Cen Jung Tjhai, Marcel Ambroze +2 more

In many modern communication systems, the full benefits of error-correction coding are only realised if the decoder is able to utilise soft decision decoding. In this chapter, we give both approximate and exact bounds on the performance of soft decision decoding compared to hard decision decoding. The effects of soft decision quantisation are explored as a function of the number of quantisation levels. Examples are given of the different performance achieved using soft and quantised soft decision decoding for (100,50) and (200,100) binary codes. A modified version of the near maximum likelihood decoder, the Dorsch decoder described in Chap. 15 , is presented for hard decision decoding. The performance improvements achieved by the decoder, compared to bounded distance decoding, are evaluated for some BCH codes. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.